Decomposition algebras and axial algebras

@article{Medts2020DecompositionAA,
  title={Decomposition algebras and axial algebras},
  author={T. D. Medts and Simon F. Peacock and S. Shpectorov and Michiel Van Couwenberghe},
  journal={Journal of Algebra},
  year={2020},
  volume={556},
  pages={287-314}
}
  • T. D. Medts, Simon F. Peacock, +1 author Michiel Van Couwenberghe
  • Published 2020
  • Mathematics
  • Journal of Algebra
  • Abstract We introduce decomposition algebras as a natural generalization of axial algebras, Majorana algebras and the Griess algebra. They remedy three limitations of axial algebras: (1) They separate fusion laws from specific values in a field, thereby allowing repetition of eigenvalues; (2) They allow for decompositions that do not arise from multiplication by idempotents; (3) They admit a natural notion of homomorphisms, making them into a nice category. We exploit these facts to strengthen… CONTINUE READING
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